Only Apple TVs with tvOS can run VPN apps, which means AppleTV HD and all generations of Apple TV 4K. Earlier Apple TVs — first, second, and third generation — do not support third-party apps. If you want a VPN for those TVs, you’ll have to get crafty. Here are some methods you can use:
Yes, you can download a VPN app on Apple TV HD or Apple TV 4K. You can do that via the App Store — just install them like any other map. Older generations of Apple TV can only use a VPN connection that is shared with them via a router or another device.